# GMAT Tip of the Week: Gary Johnson, Aleppo, and What To Do When Your Mind Goes Blank

Arguably the biggest news story this week was presidential hopeful Gary Johnson’s reply to a foreign policy question. “What is Aleppo?” is what Johnson responded, his mind evidently blanking on the epicenter of Syrian civil war and its resulting refugee crisis. And regardless of your opinion of Johnson’s fitness to be the architect of American foreign policy, there’s one major lesson there for your GMAT aspirations:

In pressure situations, it’s not uncommon for your brain to fail you as you “blank” on a concept you know (or should know). So it’s important to have strategies ready for that moment that very well may come to you. To paraphrase the Morning Joe question to Johnson:

What would you do about “Aleppo?”

Meaning: what would you do if your mind were to go blank on an important GMAT rule or formula?

There are four major strategies that should be in your toolkit for such a situation:

1) Test Small Numbers
You should absolutely know formulas like exponent rules or relationships like that between dividend, divisor, and remainder in division, but sometimes your mind just goes blank. In those cases, remember that math rules are logically-derived, not arbitrarily ordained! Math rules will hold for all possible values, so if you’re unsure, test numbers. For example, if you’re forced to solve something like:

(x^15)(x^9) =

And you’ve blanked on what to do with exponents, try testing small numbers like (2^2)(2^3). Here, that’s (4)(8) = 32, which is 2^5. So if you’re unsure, “Do I add or multiply the exponents?” you should see from the small example that you definitely don’t multiply, and that your hunch that, “Maybe I add?” works in this case, so you can more confidently make that decision.

When integer y is divided by integer z, the quotient is equal to x. Which of the following represents the remainder in terms of x, y, and z?

(A) x – yz
(B) zy – x
(C) y – zx
(D) zy – x
(E) zx – y

Many students memorize equations to organize dividend, divisor, quotient, and remainder, but in the fog of war on test day it can even be difficult to remember which element of the division problem is the dividend (it’s the number you start with) and which is the divisor (it’s the one you divide by). So if your mind has blanked on any part of the equation or on which element is which, just test it with small numbers to remind yourself how the concept works:

11 divided by 4 is 2 with a remainder of 3. How do you get to the remainder? You take the 11 you started with and subtract the 8 that you get from taking the divisor of 4 and multiplying it by the quotient of 2. So the answer is y (what you started with) minus zx (the divisor times the quotient), or answer choice C.

Simply put, if you blank on a rule or concept, you can test small numbers to remind yourself how it works.

2) Use Process of Elimination and Work Backwards From the Answer Choices
One beautiful thing about the GMAT is that, while in “the real world” if you need to know the Pythagorean Theorem and blank on it, you’re out of luck (well, unless you have a Google-enabled Smartphone in your pocket which you almost certainly do…), on the GMAT you have answer choices as assets. So if your own work stalls in progress, you can look to the answer choices to eliminate options you know for sure you wouldn’t get with that math:

What is x^5 + x^6? You know you don’t add or multiply those exponents, so even if you don’t see to factor out the common x^5, you could eliminate answer choices like x^11 and x^30.

Or you can look to the answer choices to see if they help you determine how you’d apply a rule. For example, if a problem forces you to employ the side ratios for a 45-45-90 triangle and you’ve forgotten them, the presence of some square roots of 2 in the answer choices can help you remember. The square root of 2 is greater than 1, and two sides must match, so if someone spots you “the rule includes a square root of 2” the only thing it can really be is the ratio x : x : x(√2)

Gary Johnson should have been so lucky – had the question been posed as, “What would you do about Aleppo, which is either a DJ on the new Drake album; the epicenter of the Syrian crisis; or a new restaurant in the Garment District?” he would get that question right every single time. Answer choices are your friends…when you blank, consult them!

3) Think Logically
Similar to that 45-45-90 “what else could it be?” logic, many times when you blank on a rule, you can work your way to either the rule itself or just to the answer by thinking logically about it. For example, if you end up with math that includes a radical sign in the denominator and can’t quite remember the steps for rationalizing the denominator:

What is 1/(1 – √2)?

(A) √2
(B) 1 – √2
(C) 1 + √2
(D) -1 – √2
(E) √2 – 1

Not all is lost! Sure, algebraically you should multiply the numerator and the denominator by the conjugate (1 + 2) but you can also logically work with this one. The numerator is 1, and the denominator is 1 – the square root of 2. You know that 2 is between 1 and 2, so what do you know about the denominator? It’s negative, and it’s a fraction (or decimal), so once you’ve taken 1 divided by that, your answer must be a negative number to the left of -1 – only answer choice D would work. So, yeah, you blanked on the steps, but you can still employ logic to back into the answer.

4) Write Down Everything You Know
Blanking is particularly troublesome because it’s that moment of panic. You’re trying to retrace your mental steps and the answer is elusive; it’s a moment you’re not in control of at that point. So take control! The more you’re actively working – jotting down other related formulas or facts you know, working on other facets of the diagram or problem and saving that step for last, etc. – the more you’re controlling, or at least actively managing, the situation.

Gary Johnson couldn’t get away with a “Who Wants to Be a Millionaire?” style talk-through-it (“Um, I know it’s not the name of any congressmen; it’s not Zika, it’s not…”) without looking dumb, but no one is going to audit your scratchwork and release it to Huffington Post, so you’re free to jot down half-baked thoughts and trial calculations to your heart’s content. Actively manage the situation, and you can work your way through that dreaded “my mind is blank” moment.

So learn from Gary Johnson. No matter how much you’ve prepared for your GMAT, there’s a chance that your mind will go blank on something you know that you know, but just can’t recall in the moment. But you have options, so heed the wisdom above, and let Trump or Clinton handle the gaffes for the day while you move on confidently to the next question.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTubeand Twitter!

By Brian Galvin.

# GMAT Geometry Practice Questions and Problems

Would you call yourself a math person? If so, you’ll be glad to know that there are plenty of algebra, geometry, arithmetic, and other types of math problems on the GMAT. Perhaps you like math but need a little review when it comes to the topic of geometry. If so, learn some valuable tips on how to prep for GMAT geometry problems before you get started studying for the exam.

Learn and Practice the Basic Geometry Formulas
Knowing some basic formulas in geometry is an essential step to mastering these questions on the GMAT. One formula you should know is the Pythagorean Theorem, which is a^2 + b^2 = c^2, where c stands for the longest side of a right triangle, while a and b represent the other two sides.

Another formula to remember is the area of a triangle, which is A = 1/2bh, where A is the area, b is the length of the base, and h is the height. The formula for finding the area of a rectangle is l*w = A (length times width equals the area). Once you learn these and other basic geometry formulas for the GMAT, the next step is to put them into practice so you know how to use them when they’re called for on the exam.

Complete Practice Quizzes and Questions
Reviewing problems and their answers and completing GMAT geometry practice questions are two ways to sharpen your skills for this section of the test. This sort of practice also helps you become accustomed to the timing when it comes to GMAT geometry questions. These questions are found within the Quantitative section of the GMAT.

You are given just 75 minutes to finish 37 questions in this section. Of course, not all 37 questions involve geometry – GMAT questions in the Quantitative section also include algebra, arithmetic, and word problems – but working on completing each geometry problem as quickly as possible will help you finish the section within the time limit. In fact, you should work on establishing a rhythm for each section of the GMAT so you don’t have to worry about watching the time.

Use Simple Study Tools to Review Problems
Another way to prepare for GMAT geometry questions is to use study tools such as flashcards to strengthen your skills. Some flashcards are virtual and can be accessed as easily as taking your smartphone out of your pocket. If you prefer traditional paper flashcards, they can also be carried around easily so you can review them during any free moments throughout the day. Not surprisingly, a tremendous amount of review can be accomplished at odd moments during a single day.

In addition, playing geometry games online can help you hone your skills and add some fun to the process at the same time. You could try to beat your previous score on an online geometry game or even compete against others who have played the same game. Challenging another person to a geometry game can sometimes make your performance even better.

Study With a Capable Tutor
Preparing with a tutor can help you to master geometry for GMAT questions. A tutor can offer you encouragement and guide you in your studies. All of our instructors at Veritas Prep have taken the GMAT and earned scores that have put them in the 99th percentile of test-takers. When you study with one of our tutors, you are learning from an experienced instructor as well as someone who has been where you are in the GMAT preparation process.

Our prep courses instruct you on how to approach geometry questions along with every other topic on the GMAT. We know that memorizing facts is not enough: You must apply higher-order thinking to every question, including those that involve geometry. GMAT creators have designed the questions to test some of the skills you will need in the business world.

Taking a practice GMAT gives you an idea of what skills you’ve mastered and which you need to improve. Our staff invites you to take a practice GMAT for free. We’ll give you a score report and a performance analysis so you have a clear picture of what you need to focus on. Then, whether you want help with geometry or another subject on the GMAT, our team of professional instructors is here for you.

# Quarter Wit, Quarter Wisdom: The Power of Deduction on GMAT Data Sufficiency Questions

In a previous post, we have discussed how to find the total number of factors of a number. What does the total number of factors a number has tell us about that number? One might guess, “Not a lot,” but it actually does tell us quite a bit! If the total number of factors is odd, you know the number must be a perfect square. If the total number of factors is even, you know the number is not a perfect square.

We know that the total number of factors of a number A (prime factorised as X^p * Y^q *…) is given by (p+1)*(q+1)… etc.

So, if we know that a number has, say, 6 total factors, what can we say about the number?

6 = (p+1)*(q+1) = 2*3, so p = 1 and q = 2 or vice versa.

A = X^1 * Y^2 where X and Y are distinct prime numbers.

Today, we will look at a data sufficiency question in which we can use factors to deduce much more information than what we might first guess:

When the digits of a two-digit, positive integer M are reversed, the result is the two-digit, positive integer N. If M > N, what is the value of M?

Statement 1: The integer (M – N) has 12 unique factors.
Statement 2: The integer (M – N) is a multiple of 9.

With this question, we are told that M is a two-digit integer and N is obtained by reversing it. So if M = 21, then N = 12; if M = 83, then N = 38 (keeping in mind that M must be greater than N). In the generic form:

M = 10a + b and N =10b + a (where a and b are single-digit numbers from 1 to 9. Neither can be 0 or greater than 9 since both M and N are two-digit numbers.)

We also know that no matter what M and N are, M > N. Therefore:

10a + b > 10b + a
9a > 9b
a > b

Let’s examine both of our given statements:

Statement 1: The integer (M – N) has 12 unique factors.

First, let’s figure out what M – N is:

M – N = (10a + b) – (10b + a) = 9a – 9b

Say M – N = A. This would mean A = 9(a-b) = 3^2 * (a-b)

The total number of factors of A where A = X^p * Y^q *… can be calculated using the formula (p+1)*(q+1)* …

We know that A has 3^2 as a factor, so X = 3 and p = 2. Therefore, the total number of factors would be (2+1)*(q+1)*… = 3*(q+1)*… = 12, so (q+1)*… must be 4.

Case 1:
This means q may be 3 so that (q+1) is 4. Since a-b must be less than or equal to 9 and must also be the cube of a number, (a-b) must be 8. (Note that a-b cannot be 1 because then the total number of factors of A would only be 3.)

So, a must be 9 and b must be 1 in this case (since a > b). The integers will be 91 and 19, and since M > N, M = 91.

Case 2:
Another possibility is that (a-b) is a product of two prime factors (other than 3), both with the power of 1. In that case, the total number of factors = (2+1)*(1+1)*(1+1) = 12

Note, however, that the two prime factors (other than 3) with the smallest product is 2*5 = 10, but the difference of two single-digit positive integers cannot be 10. This means that only Case 1 can be true, therefore, Statement 1 alone is sufficient. This is certainly not what we expected to find from just the total number of factors!

Statement 2: The integer (M – N) is a multiple of 9.

M – N = (10a + b) – (10b + a) = 9a – 9b, so M – N = 9 (a-b) . This is already a multiple of 9.

We get no new information with this statement; (a-b) can be any integer, such as 2 (a = 5, b = 3 or a = 7, b = 5), etc. This statement alone is insufficient, therefore our answer is A.

Don’t take the given data of a GMAT question at face value, especially if you are expecting questions from the 700+ range. Ensure that you have deduced everything that you can from it before coming to a conclusion.

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

# Important GRE Math Formulas to Know Going Into the Exam

The Quantitative Reasoning section is just one of three parts of the GRE. In this section, students must answer algebra, arithmetic, geometry, and data analysis questions. In order to prep for this section of the test, students must take time to learn some GRE math formulas, as these formulas aren’t provided on the test. Check out some examples of math formulas for GRE questions and get some tips on how to master this section of the exam.

Examples of GRE Math Formulas

• Slope-intercept: y = mx + b
• Distance = Rate * Time or D = RT
• Average Speed = Total Distance/Total Time
• For squares: Perimeter = 4s (side); Area = s2
• For rectangles: Area = Length * Width or A= lw; Perimeter= 2l + 2w
• For polygons: Total degrees = 180(n-2), where n = the number of sides
• For circles: Area = πr2 , Circumference = 2πr

Tips for the Quantitative Section
As a student works through this portion of the test, it’s helpful to scan through the answer options and eliminate those that are clearly incorrect. Crossing out these options helps to make a math problem more manageable for a student. Plus, the student doesn’t have to waste time considering answer options that are definitely not going to work.

A second tip is to work problems out on scrap paper. This is especially beneficial when working on word problems – a student is able to see all of the parts of a problem without having to mentally juggle a lot of figures. Furthermore, if a student arrives at an answer that doesn’t match up with any of the options, they can go back to the work on the scrap paper to find the mistake.

Students may want to get into the habit of estimating the answer before considering any of the answer options. This gives the student a rough idea of what the answer looks like before choosing the official solution from the multiple options.

In order to save test time, it’s also a good idea for students to skip extremely puzzling questions and return to them later on in the test period. A student who spends too much time on one problem in the quantitative reasoning section is likely to run out of time before finishing the rest of the section. Students who take the computer-delivered version of the GRE are able to use a convenient “mark and review” tool that helps them to remember the questions that were skipped and go back to them.

Studying for the Quantitative Section
Memorizing math formulas for GRE questions is just one of the effective ways to study for the GRE. Working on practice math problems is another way to prep for the test. This gives a student the opportunity to practice using those math formulas. As they work through a variety of problems, students can become familiar with when to use a particular GRE math formula.

Some students find it helpful to make flash cards with math formulas on them. They can quiz themselves by holding up a flash card with a GRE math formula on it. Next, the student should successfully complete a problem using that formula.

Online math games are another study tool used by many students. Games can be a fun way for students to refresh their algebra skills or get reacquainted with the rules of geometry. Some students like to pair with another person to play these types of math games. Competing with a friend to see who can score more points and end up with more correct answers can be motivating to many students who plan to take the GRE. Plus, it’s always helpful to hear encouraging words from a friend.

All of our GRE instructors at Veritas Prep have taken the exam and achieved impressive scores. They are familiar with the subtleties of this challenging test. In short, our students learn from instructors who know what it takes to master the Quantitative Reasoning section as well as the other sections on the GRE. Our instructors help students to learn the math formulas they need to know to take on the test with confidence. We offer in-person and online courses in which students can get test-taking strategies from the experts. Contact Veritas Prep today!

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